The Food and Drug Administration is requiring manufacturers of the most widely prescribed painkillers to provide extensive training to doctors in an attempt to reduce the number of patients who become addicted, and stem the ongoing opioid crisis.

The agency notified 74 manufacturers of so-called immediate-release opioids this week that their drugs will now be subject to the tougher requirements, although doctors would not be compelled to take part in the training.

The medications, which include Vicodin and Percocet, often combine oxycodone or hydrocodone with less powerful painkillers like ace...